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Open book, calculators allowed. SHOW ALL OF YOUR WORKING.
1. [5 points ] Write the function ( ) = 2 2 + 12 , 14 in the form ( ) = ( , )2 +
by completing the square. [Hint: multiply out your answer to check that it
equals 2 2 + 12 , 14.]
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Solution:
( ) = 2 2 + 12 , 14
= 2 ( 2 + 6 , 7)
= 2 ( 2 + 6 + 9 , 9 , 7)
= 2 ( 2 + 6 + 9 , 16)
= 2 ( + 3)2 , 32
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2. [2 points ] Find the zeros of the function ( ).
2 +12 , 14 = 2( +7)( , 1) = 0 so zeros are = ,7 1.
Solution: Factor 2
One point for each correct zero.
3. [3 points ] Draw the graph of = 2 2 + 12 , 14. Identify the -intercept, the intercepts and the vertex.
Solution: The -intercept is (0 ,14) (1 point), the -intercepts are (,7 0)
and (1 0) (1 point for plotting both correctly), while the vertex is (,3 ,32)
(1 point for plotting correctly). Join these dots with a smooth parabola.
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